Question

A company that manufactures brackets for an automaker regularly selects brackets from the production line and performs a torque test. Let X equal the torque of a randomly selected bracket and assume that X is norm(mean = µ, sd = σ). We shall collect a simple random sample of n = 10 observations.

[1] 58.6 59.0 59.3 58.5 58.6 58.7 59.4 59.5 59.6 58.4

(a) What does the parameter µ represent in this context?

(b) Report a point estimate for µ. (You are not required to derive the point estimator.)

(c) Is your estimate unbiased? Justify your answer.

(d) Use the observations to find a 99.9% two-sided confidence interval for µ. Be sure to address all five (5) salient components of a confidence interval.

Answer 1

(a) What does the parameter µ represent in this context?

µ represent population mean of bracket

(b) Report a point estimate for µ. (You are not required to derive the point estimator.)

sample mean is point estimator for µ

= 58.96

(c) Is your estimate unbiased? Justify your answer.

yes, sample mean is unbiased estimator for µ

(d) Use the observations to find a 99.9% two-sided confidence interval for µ.

(Xbar +- t * sd/sqrt(n))

(58.272,59.648)